A077250 - OEIS

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A077250

Bisection (odd part) of Chebyshev sequence with Diophantine property.

6

11, 103, 1019, 10087, 99851, 988423, 9784379, 96855367, 958769291, 9490837543, 93949606139, 930005223847, 9206102632331, 91131021099463, 902104108362299, 8929910062523527, 88396996516872971, 875040055106206183, 8662003554545188859, 85744995490345682407

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OFFSET

0,1

COMMENTS

a(n)^2 - 24*b(n)^2 = 25, with the companion sequence b(n) = A077249(n).

The even part is A077409(n) with Diophantine companion A077251(n).

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

Index entries for linear recurrences with constant coefficients, signature (10,-1).

FORMULA

a(n) = 10*a(n-1)- a(n-2), a(-1)=7, a(0)=11.

a(n) = 2*T(n+1, 5)+T(n, 5), with T(n, x) Chebyshev's polynomials of the first kind, A053120. T(n, 5)= A001079(n).

a(n) = sqrt(25 + 24*A077249(n)^2).

G.f.: (11-7*x)/(1-10*x+x^2).

EXAMPLE

103 = a(1) = sqrt(24*A077249(1)^2 + 25) = sqrt(24*21^2 + 25) = sqrt(10609) = 103.

MATHEMATICA

CoefficientList[Series[(11 - 7 z)/(z^2 - 10 z + 1), {z, 0, 200}], z] (* Vladimir Joseph Stephan Orlovsky, Jun 11 2011 *)

PROG

(PARI) a(n)= 2*polchebyshev(n+1, 1, 5)+polchebyshev(n, 1, 5) \\ Charles R Greathouse IV, Jun 11 2011

(PARI) Vec((11-7*x)/(1-10*x+x^2) + O(x^30)) \\ Colin Barker, Jun 15 2015

CROSSREFS

Sequence in context: A016133 A287833 A155594 * A356128 A173851 A358340

Adjacent sequences: A077247 A077248 A077249 * A077251 A077252 A077253

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Nov 08 2002

STATUS

approved